¹ *Source: wiktionary.com*

### Definition of Subspaces

**1.** subspace [n] - See also: subspace

### Lexicographical Neighbors of Subspaces

### Literary usage of Subspaces

Below you will find example usage of this term as found in modern and/or classical literature:

**1.** *Topics in the Geometric Theory of Integrable Mechanical Systems* by Robert Hermann (1984)

"EULER-ARNOLD VECTOR FIELDS THAT ARE TANGENT TO THE JACOBI ** Subspaces** Let C be a
... be a Jacobi triple of linear subspaces. Let J be the associated Jacobi ..."

**2.**

*Geometry of Non-Linear Differential Equations, Backlund Transformations, and*by Robert Hermann (1977)

"A2 = vd A Vd a space of skew-symmetric bilinear maps VxV + R and so forth. For each integer m, let Gm(V) denote the space of n-dimensional linear subspaces ..."

**3.**

*Topics in Physical Geometry*by Robert Hermann (1988)

"LAX REPRESENTATIONS FOR CERTAIN VECTOR FIELDS ON LINEAR

**OF LIE ALGEBRAS As I have mentioned, the most important situation for Integrable Systems ..."**

**Subspaces****4.**

*Real Analysis*by Andrew M. Bruckner, Judith B. Bruckner, Brian S. Thomson (1997)

"13:10.6 In the proof of Theorem 13.33 we left out some details involving "subsequences of subsequences." How might these be provided? 13.11 Closed

**..."**

**Subspaces****5.**

*Convex Optimization and Euclidean Distance Geometry*by Jon Dattorro (2005)

"E.3.1 Four subspaces We summarize the orthogonal projectors projecting on the four fundamental subspaces: for ..."

**6.**

*Elementary Real Analysis*by Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner (2001)

"13.8.2

**of a Complete Space Suppose now we wish to prove that the space C[a, b] is complete. We could argue exactly as we did with M[a, ..."**

**Subspaces****7.**

*Proceedings of the Berkeley-Ames Conference on Nonlinear Problems in Control*by Louis R. Hunt, Clyde Martin (1984)

"Thus, the classical power method is actually an iteration on the set of one-dimensional subspaces of Rn, and the points of ..."